Ugh, going by what floats around online, it's gotta be the 'Turtle Power' chant from the 80s cartoon theme song. People slap that on everything. But honestly? The most shared one in my circles is from 'City At War' in the Mirage comics: 'Tonight I dine on turtle soup!' from the Shredder. It's brutal and it's just such a perfect villain line, you see it as reaction images all the time when someone's about to win an argument.
That and 'Cowabunga!' obviously, but that's almost cheating, it's the brand slogan. I've seen 'I love being a turtle!' from the first live-action movie make a comeback recently, probably because of the nostalgia wave. It's the delivery that sells it, the sheer joy.
For something a little deeper, fans of the 2012 series and the 'Rise' show circulate the brotherly bickering quotes a lot—like Leo's 'We're a team!' exasperation or Raph's 'I'm the awesome one!' boast. It's less about a single iconic line and more about capturing their dynamic.